Mathematical modeling suggests pre-existing immunity to SARS-CoV-2

Abstract

Mathematical models have largely failed to predict the unfolding of the COVID-19 pandemic. We revisit several variants of the SEIR-model and investigate various adjustments to the model in order to achieve output consistent with measured data in Manaus, India and Stockholm. In particular, Stockholm is interesting due to the almost constant NPI’s, which substantially simplifies the mathematical modeling. Analyzing mobility data for Stockholm, we argue that neither behavioral changes, age and activity stratification nor NPI’s alone are sufficient to explain the observed pandemic progression. We find that the most plausible hypothesis is that a large portion of the population, between 40 to 65 percent, have some protection against infection with the original variant of SARS-CoV-2.

Influenza A H1N1–mediated pre-existing immunity to SARS-CoV-2 predicts COVID-19 outbreak dynamics

“…Second, the mathematical model can only suggest a range of pre-immunity levels that are likely to be true in reality. Both SEIR models we used in earlier work (11,12) and the method developed here are crude tools, and the results should be interpreted with caution. However, SIR (susceptible, infective, recovered) and SEIR models that did not include pre-immunity completely failed to predict the dynamics of SARS-CoV-2 spread (11,12); pre-immunity levels that we here found to be different in Stockholm versus in India.…”

“…Both SEIR models we used in earlier work (11,12) and the method developed here are crude tools, and the results should be interpreted with caution. However, SIR (susceptible, infective, recovered) and SEIR models that did not include pre-immunity completely failed to predict the dynamics of SARS-CoV-2 spread (11,12); pre-immunity levels that we here found to be different in Stockholm versus in India. This is the main mathematical argument for the existence of a pre-existing immunity, the exact level of which is hard to estimate with certainty.…”

“…To test this hypothesis, we used mathematical models to study the effects of factors such as nonpharmacological interventions, age, interactive patterns, mobility, and pre-immunity on viral outbreaks. It proved impossible to match modeled and real data without incorporating a pre-existing immunity level of 50–60% (11, 12). We therefore set out to identify the source of the pre-immunity.…”

A note on variable susceptibility, the herd-immunity threshold and modeling of infectious diseases

“…According to table 3 in the report, the number of deaths and peak ICU capacity can be reduced by 50% and 81%, respectively, in the most effective NPI-scenario, which certainly goes beyond what was implemented in Sweden. However, as of February 2021, when the original Wuhan-strain was declining [25], these reduced predictions overestimate the actual figure by a factor of roughly 4 (deaths) and 10 (ICU) (when directly translated to Stockholm County).…”

“…[9] and set T incubation = 4 and T infectious = 3. It then follows that the generation time equals where the generation time is the average time it takes from a person getting infected until that person infects others (see equation (5) in [25]). Note that this is consistent with the choice of T generation in previous sections.…”